Problem 131 - General Chemistry: Principles and Modern Applications

Question

When \(\mathrm{NH}_{4} \mathrm{Cl}\) dissolves in a test tube of water, the test tube becomes colder. Is the magnitude of \(\Delta \mathrm{H}_{\text {lattice }}\) for \(\mathrm{NH}_{4} \mathrm{Cl}\) larger or smaller than the sum of \(\Delta \mathrm{H}_{\text {hydration }}\) of the ions?

Step-by-Step Solution

Answer

The magnitude of \(\Delta H_{\text{lattice}}\) for \(\mathrm{NH}_{4} \mathrm{Cl}\) is larger than the magnitude of the sum of \(\Delta H_{\text{hydration}}\) for the ions.

Step 1: Understand the process of dissolution

The process of dissolution of a substance can be divided into two basic steps: i.e., breaking the lattice (endothermic process, \(\Delta H_{\text{lattice}}\)) and hydration of ions (exothermic process, \(\Delta H_{\text{hydration}}\)). The overall enthalpy change during this process is the algebraic sum of \(\Delta H_{\text{lattice}}\) and \(\Delta H_{\text{hydration}}\): \(\Delta H_{\text{dissolution}} = \Delta H_{\text{lattice}} + \Delta H_{\text{hydration}}\).

Step 2: Understand the relationship between enthalpy change and temperature change

If the enthalpy change of dissolution (\(\Delta H_{\text{dissolution}}\)) is endothermic (i.e., if it absorbs heat), the temperature of the surroundings (in this case, the test tube of water) decreases, making the solution feel cold to the touch. If \(\Delta H_{\text{dissolution}}\) is exothermic (i.e., if it releases heat), the temperature of the surroundings increases, making the solution feel warm.

Step 3: Apply knowledge to solve the problem

Given that the test tube feels cold when \(\mathrm{NH}_{4} \mathrm{Cl}\) dissolves, the enthalpy change of dissolution must be endothermic. By rearranging the equation in Step 1, we find that \(\Delta H_{\text{lattice}} = \(\Delta H_{\text{dissolution}} - \Delta H_{\text{hydration}}\). Since \(\Delta H_{\text{dissolution}}\) is positive (as the process is endothermic) and \(\Delta H_{\text{hydration}}\) is negative (as the process is exothermic), the magnitude of \(\Delta H_{\text{lattice}}\) must be larger than the magnitude of \(\Delta H_{\text{hydration}}\) in order for their sum to be positive.

Key Concepts

Dissolution Process

Understanding the dissolution process is fundamental in grasping why certain substances change the temperature of their surroundings when they dissolve in a solvent like water. Dissolution involves two key steps: first, breaking apart the solid's lattice, which requires energy (endothermic), and second, the hydration of ions, where water molecules attach to the ions, releasing energy (exothermic).

The overall enthalpy change of dissolution, denoted as (Delta H_{text{dissolution}}), is the sum of these two steps:(Delta H_{text{dissolution}} = Delta H_{text{lattice}} + Delta H_{text{hydration}}). When a substance like ammonium chloride ((NH_{4} Cl)) dissolves and the test tube gets colder, it indicates that the energy needed to break the lattice is not fully compensated by the energy released during hydration, leading to an overall absorption of heat from the surroundings.

Lattice Energy

Lattice energy is a term used to describe the amount of energy required to separate one mole of an ionic solid into its gaseous ions. It's a measure of the strength of the forces holding the ions in the lattice, and it is always a positive value because breaking bonds requires an input of energy. High lattice energy implies a strong attraction between the ions, and, as such, more energy is needed to overcome these attractions.

In the case of ammonium chloride ((NH_{4} Cl)), a high lattice energy accounts for the initial endothermic step of dissolution where the ionic bonds are broken, resulting in the observed cooling effect.

Hydration Enthalpy

Hydration enthalpy, on the other hand, is associated with the energy change when gaseous ions are surrounded by water molecules and go into solution. This process is normally exothermic; water molecules stabilize the ions through electrostatic interactions, and as a result, energy is released. This released energy can sometimes be enough to make the entire dissolution process exothermic if the hydration enthalpy is greater than the lattice energy.

However, in our ammonium chloride example, the cold feeling of the test tube indicates that the hydration enthalpy is not sufficient to offset the large lattice energy, suggesting the net process involves the absorption of heat from the surroundings, thus being overall endothermic.

Thermodynamics in Chemistry

Thermodynamics in chemistry is the study of the energy and heat involved in chemical reactions and phase changes. It involves concepts like enthalpy ((Delta H)), entropy, and Gibbs free energy. The enthalpy change gives us insight into the heat exchange with the surroundings during a reaction or a phase change. In the dissolution of ammonium chloride, the thermodynamic principles indicate that the total enthalpy can either absorb heat from the surroundings (endothermic) or release heat to them (exothermic).

The understanding of these thermodynamic processes is crucial in predicting the outcome of reactions and the study of energy changes in chemical processes, helping us to manipulate reactions and design substances with desired thermal properties.